CN120266051A - Method and device for generating second harmonic radiation by means of a crystal with non-critical phase matching and controlling the relative phase between a fundamental frequency electromagnetic field and an electromagnetic field with double frequency - Google Patents

Abstract

A method for generating second harmonic radiation from fundamental radiation, comprising the following steps: providing one or more nonlinear crystals (C) that meet the conditions for second harmonic generation (SHG) by noncritical phase matching; providing an optical phase actuator (A) that is located upstream or downstream of the nonlinear crystal (C) relative to the principal optical axis (O) of the nonlinear crystal, and determining the parameters of the optical actuator (A) for which the measured power is maximum relative to the power measured during the execution of the multiple measurements by controlling the temperature of the optical actuator (A) itself or by applying an electric field or a magnetic field to the optical actuator (A) to change one or more of the parameters of the optical actuator (A) over time.

Description

Method and device for generating second harmonic radiation by means of a crystal with non-critical phase matching and controlling the relative phase between a fundamental electromagnetic field and an electromagnetic field with doubled frequency

Technical Field

The invention relates to a device for generating second harmonic radiation. In particular, it relates to generating a field E _2ω having an angular frequency of 2ω from an electromagnetic field E _ω having an angular frequency of ω by passing light through one or more birefringent nonlinear crystals under non-critical phase matching conditions, i.e., under which phase matching in the propagation of fields E _ω and E _2ω in the nonlinear crystals occurs by propagating the fields in the same direction such that the refractive index change caused by birefringence coincides with the refractive index change caused by dispersion. In order to maintain this phase matching condition also in the case of propagation through multiple crystals or multiple passes through the same crystal, with the aim of maximizing the final power of the second harmonic radiation, we propose an actuator which allows to vary in a controlled way the relative phase between the two fields at the input of the SHG (second harmonic generation) doubling stage after the first, by acting on the temperature of the other birefringent crystal

Solutions for improving nonlinear conversion efficiency based on sequential formation of a plurality of crystals, in combination with actuators for controlling the relative phases, and solutions for laterally confining the laser beam within the nonlinear crystals have also been proposed.

Background

In order to obtain electromagnetic radiation E _2ω having a frequency twice the electromagnetic field E _ω of a given angular frequency ω, a common solution is to use a Second Harmonic Generation (SHG) process, which is based on the propagation of the field E _ω in a nonlinear medium having a non-zero secondary electric susceptibility coefficient (χ ₂ +.0).

The magnitude of the second harmonic field E _2ω is proportional to the length L of the nonlinear crystal passed through, provided that a given condition between the phases of the fundamental frequency field E _ω and the second harmonic field E _2ω is satisfied. Only in this condition, known as phase matching, does the contributions from various locations along the propagation direction to the field E _2ω constructively interfere, maximizing the size of the second harmonic field at the crystal output.

This phase matching condition corresponds to the wave vector requiring two fields E _ω and E _2ω The following relationship is satisfied:

Is the vector of wave vectors, is the scalar product operator between vectors, λ=2ρc/ω is the wavelength, and n is the refractive index of the medium.

For a co-linear wave vector,The phase matching condition of equation 1 reduces to:

k_2ω＝2k_ω.

this corresponds to the following condition of refractive index:

n_2ω＝n_ω。

In order to satisfy the phase matching condition, one common method is to use a birefringent nonlinear crystal. The latter is an anisotropic medium in which the refractive index depends not only on the wavelength λ of the radiation propagating therein and the temperature T of the crystal, but also on the propagation direction and the polarization of the radiation

In particular, two mutually orthogonal polarization modes are defined, ordinary polarizationAnd extraordinary polarization

In uniaxial birefringent crystals, the refractive index versus wave vector for extraordinary polarizationThere is a dependence of the angle θ between the axes of the crystal, n _e = n (λ, θ), whereas for ordinary polarization the refractive index is independent of the propagation direction.

In view of the dependence of refractive index on frequency, temperature and angle in birefringent media, two main strategies to obtain phase matching are determined:

control of the angle of incidence ("angle tuning phase matching"). In this case, for a given temperature, the vector indicating the propagation direction of the fundamental frequency field E _ω is modified An angle θ with an optical axis of the crystal. Thus, the polarization of field E _ω will beAndIs a linear combination of (a) and (b). In this case, although the more general phase matching condition is satisfiedBut due to the dependence of the refractive index on the angle theta,AndNot parallel.AndThe fact of non-parallelism introduces a so-called walk-off phenomenon, i.e. the profile of the beam E _2ω is perpendicular toIn the transverse direction of (a), in the direction of (a) byAndA defined in-plane stretching. Such asymmetry is usually corrected by using cylindrical lenses, prisms, or the like. Another consequence of walk-off is a reduced spatial overlap between the fundamental and second harmonic fields, resulting in reduced conversion efficiency.

Temperature control ("temperature tuning phase matching"). In this case, the vector is caused toCoincident with one of the principal axes of the crystal. This approach is also defined as angle non-critical phase matching, or simply non-critical phase matching, because there is no critical dependence on angle. By varying the temperature in a controlled manner, the value T thereof is determined such that at a given fundamental field frequency ω there is: Or (b) Thereby achieving maximum second harmonic generation efficiency.

This method has the advantage of minimizing walk-off compared to controlling the angle of incidence. In fact, when the vectorVector when coincident with one of the principal axes of the crystalWill also coincide with the same optical axis under plane wave approximation.

More realistically, the incident laser beam is not a plane wave, but has a gaussian profile, focused by a lens at the central portion of the crystal, to increase the radiation intensity and facilitate the second harmonic conversion process. In this case, it is necessary to consider further effects affecting the phase matching condition, which are linked to the different coughing phases of the fundamental frequency field and the second harmonic field accumulated during propagation, which results in a gradual increase of the phase shift with increasing crystal length.

A further cause of phase shift is accumulation of walk-off in the nonlinear medium (especially in the case of angle critical phase matching) and thermal effects that lead to the formation of temperature gradients in the crystal as the second harmonic field power increases. This thermal effect is particularly important in the case of temperature phase matching, since the phase matching conditions can only be met locally, resulting in a reduction of the overall conversion efficiency.

Although the size of the second harmonic field should ideally be proportional to the crystal length (E _2ω. Alpha. L), in practice, it is advantageous to increase the crystal length L to the maximum imposed by the coherence length in the presence of a phase shift, L _c =pi/. DELTA.k, whereDetermined by the phase matching condition of equation 1.

Furthermore, in practice, there is a further technical limitation to the maximum length L of the nonlinear medium, which is related to the production method of crystal growth.

In order to solve these problems and achieve high conversion efficiency in the SHG process, several solutions are proposed:

A first solution consists in placing the crystal in an optical cavity (see for example the article Ashkin1966 a. Ashkin et al, "Resonant optical second harmonic generation and mixing", IEEE Journal of Quantum Electronics, volume 2, phase 6, pages 109-124, 1966, month 6 ,doi:10.1109/JQE.1966.1074007],Berger1997[V.Berger,"Second-harmonic generation in monolithic cavities",J.Opt.Soc.Am.B14,1351-1360(1997)],McDonagh2007[McDonagh2007 L.McDonagh et al ,"Low-noise 62WCW intracavity-doubled TEM00 Nd:YVO4 green laser pumped at 888nm",Opt.Lett.32(7),802–804(2007)]), in order to achieve an effective increase in the intensity of the fundamental frequency field across the crystal by exploiting the resonance conditions between the optical cavity and the fundamental frequency field.

This approach is widely used because it can significantly increase the power of the second harmonic radiation available in compact systems where only a single nonlinear crystal is used.

However, the use of resonant cavities at high power may create problems because the high intensity of radiation accumulated within the cavity may lead to instability of the thermal properties and instability of the photorefractive properties, as well as damage to the crystal and other optical elements present, especially in the case of high frequency second harmonic radiation (UV). In addition, mechanical stress can affect proper alignment, resulting in reduced gain introduced by the cavity.

A second solution consists in passing the light twice or more generally more through the same crystal in a non-resonant configuration by specular reflection as shown in fig. 1. The use of concave mirrors allows refocusing the light inside the crystal, avoiding chromatic dispersion that can occur when using lenses.

To maximize efficiency, the phase delay that may exist between fundamental field E ⁽ⁱ⁾ _ω and second harmonic field E ⁽ⁱ⁾ _2ω, introduced by specular reflection, dispersion of air (or other medium present between the mirror and the crystal), and propagation through any anti-reflection treatment across the crystal aperture, must be considered in any case at every ith pass out of the crystal.

Also in case of multiple non-resonant passes through the same crystal, it is necessary to consider the same problems associated with the risk of damage due to high radiation intensity under high power operating conditions, as already described for configurations with resonant cavities.

A third solution involves the use of multiple cascaded crystals. This approach is particularly advantageous when operating at high power, because the radiation intensity in a single crystal is reduced, considering a less compact system that requires multiple nonlinear crystals. By using suitable optical elements, the focusing conditions of each crystal in the sequence can be controlled according to the intensity of the second harmonic radiation already present at the entrance to avoid damage to the crystal by too high a radiation intensity.

Further, by appropriate measures, the phase matching condition in each crystal can be locally controlled, thereby optimizing the overall second harmonic generation efficiency.

In particular, it is necessary to compensate for the phase shift mainly caused by thermal effects (related to the partial absorption of SHG radiation by the crystals; see, for example, sabaeian2010[ M. Sabaeian et al ,"Investigation of thermally-induced phase mismatching in continuous-wave second harmonic generation:A theoretical model",Opt.Express 18,18732-18743(2010)])、 ] dispersion of air, the presence of anti-reflection treatments on the optical aperture of each crystal, and any other non-achromatic optical elements on the optical path.

With respect to correction of phase mismatch, various methods have heretofore been used to reestablish the optimum phase matching condition in the case of two or more passes through the same crystal or through a series of crystals to generate the second harmonic.

Of importance is the method mentioned Imeshev et al [ Imeshev G.Imeshev et al ,"Phase correction in double-pass quasi-phase-matched second-harmonic generation with a wedged crystal",Opt.Lett.23,165-167(1998)], for compensating for the phase shift introduced by specular reflection or by dispersion propagating in air as shown in FIG. 1. The solution they propose is based on using a quasi-phase-matched crystal cut at an angle, so that the optical path length in the nonlinear medium can be changed by changing the lateral displacement Δh of the crystal, as schematically shown in fig. 2. The method is suitable for quasi-phase matching crystals with inconsistent refractive indexes of a fundamental frequency field and an SHG field.

Other solutions are based on compensating for the phase shift introduced by specular reflection by using the different dispersions of the two fields in air by acting on the distance between the latter and the crystal, e.g. Yarborough et al [ Yarborough1970 J.M. Yarboroough et al ,"Enhancement of optical second harmonic generation by utilizing the dispersion of air",Appl.Phys.Lett.18,70-73(1971)].

Another strategy to compensate for walk-off in angle matched crystals caused by the different propagation of the ordinary and extraordinary polarization fields involves dividing the crystal into segments, rotating the segments such that each segment produces a walk-off in opposite directions, thereby minimizing the overall phase shift, as described by Smith et al, smith1998 a.v. Smith et al ,"Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals",J.Opt.Soc.Am.B 15,122-141(1998)]. These crystals may also be placed in contact as described in Zondy et al [ Zondy1996-J.Zondy et al ,"Walk-off-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices",Proc.SPIE 2700,Nonlinear Frequency Generation and Conversion,(1996)].

In Kumar11[ Kumar11-s.c. Kumar et al ,"High-efficiency,multicrystal,single-pass,continuous-wave second harmonic generation",Opt.Express 19,11152-11169(2011)-Kumar11], a polycrystalline device based on crystals meeting quasi-phase matching conditions is proposed in which the light is focused by a concave mirror with a suitable focal length. In this application, the thermal effect is particularly pronounced and becomes increasingly important as the second harmonic radiation power within the crystal sequence increases, while it is necessary to take into account the gradual decrease in the size of the fundamental field. To compensate for these effects, the temperature and light focusing conditions of the individual crystals are optimized in order to maximize the final power of the second harmonic radiation under global trade-off conditions. The compensation of the relative phase between the fundamental frequency field and the SHG field is achieved by acting on the position of the crystals to take into account the dispersion propagating in air between the different crystals.

Another method proposed by Liu et al [ Liu2017-x.liu et al ,"Three-crystal method for thermally induced phase mismatch compensation in second-harmonic generation",J.Opt.Soc.Am.B 34,383-388(2017)] to compensate for phase mismatch caused by thermal effects in SHG nonlinear crystals involves combining three birefringent crystals placed in sequence. In contrast, a centrally located crystal has a negative derivative of the phase shift with respect to temperature, so that the phase mismatch introduced by the thermal effect of the first crystal in the sequence can be compensated at the same temperature T, thus optimizing the efficiency of the SHG process in the second crystal. This is a passive phase shift compensation obtained by fine tuning the (micron-scale) central birefringent crystal length.

To address the inaccuracy in crystal length, the latter is tilted at a small angle until the optimum compensation conditions are reached.

In contrast, cui et al [ Cui2016-Z. Cui et al ,"Compensation method for temperature-induced phase mismatch during frequency conversion in high-power laser systems",J.Opt.Soc.Am.B 33,525-534(2016)] ] have actively corrected for phase shift in an apparatus for generating high power second harmonic radiation, which in this case is also based on a series of birefringent crystals, two crystals at the ends of the sequence for SHG, with one electro-optic crystal placed between them. By adjusting the voltage applied to the latter, as has been proposed in volume Hon1976[D.Hon,"Electrooptical compensation for self-heating in CD*A during second-harmonic generation",IEEE Journal of Quantum Electronics,, phase 2, pages 148-151, 1976], a phase shift can be introducedThis phase shift compensates for the phase shift accumulated at the output of the first crystal mainly due to thermal effects. In this way, it is possible to successfully increase the total power of the available SHG radiation and improve the temperature range over which SHG occurs and the stability to temperature variations.

One disadvantage of this approach is associated with the high voltages required (up to about 10 ⁴ V), which can lead to technical complexity of the device compared to the use of a temperature-controlled birefringent crystal sequence alone.

Disclosure of Invention

An object of the present invention is to propose an apparatus and a method for actively compensating any phase shift between the fields E _ω and E _2ω input to a nonlinear birefringent crystal for Second Harmonic Generation (SHG)Thereby solving the technical problems.

In particular, the proposed device is based on the use of another dispersive element, for example, produced by another temperature-tunable birefringent crystal. By temperature tuning, the refractive index difference of the dispersive medium for the fundamental frequency field and the SHG field can be changed, Δn (T) =n _ω(T)-n_2ω (T). By doing so, the phase shift accumulated by the two fields at the output of the dispersive element can be controlledBy placing the dispersive element at the entrance of the nonlinear crystal for SHG, compensation for phase shift can be achievedThe phase shift exists between the fundamental frequency field and the existing SHG field. In this way, the SHG efficiency can be optimized even in the case of multiple passes through the same crystal or based on the configuration of a plurality of SHG crystals in which the phase matching conditions can be satisfied independently.

A solution has also been proposed to overcome the technical limitations of nonlinear crystal length by using multiple cascaded (stacked) crystals. In order to optimize the efficiency of the SHG process, in addition to using a suitable anti-reflection treatment on the crystal aperture, it is also suggested to use a tunable dispersion element to control the relative phase between two adjacent crystals as previously describedSuch a dispersive element may be produced by, for example, a birefringent crystal, also made of the same material and having the same orientation cut as the nonlinear crystal for frequency doubling described above. Temperature control of phase actuator elements placed between frequency doubling nonlinear crystals can be precisely controlled

Furthermore, the tunable dispersion element can be fabricated with a surface having a radius of curvature to focus light inside the nonlinear crystal for SHG.

One variant of this solution envisages the use of nonlinear crystals cut in a way that they perform their own focusing function. This may be achieved, for example, by imposing a suitable radius of curvature on one or more optical apertures of the crystal.

The solutions presented above may be combined with each other to maximize the efficiency and robustness of the SHG procedure.

Drawings

Fig. 1 and 2 show schematically an arrangement for generating second harmonic radiation according to the prior art, respectively.

Fig. 3a and 3b show in schematic form two variants, respectively, of an apparatus for generating second harmonic radiation according to a first embodiment of the invention.

Fig. 4 schematically illustrates an apparatus for generating second harmonic radiation according to an alternative embodiment.

Fig. 5 and 6 show in schematic form two variants of an apparatus for generating second harmonic radiation according to a second embodiment of the invention, respectively.

Fig. 7, 8a and 8b show in schematic form a variant of the device for generating second harmonic radiation according to a third embodiment of the invention, respectively.

Fig. 9 shows in schematic form a further variant of the device for generating second harmonic radiation in fig. 4.

Fig. 10 shows in schematic form a further variant of the device for generating second harmonic radiation in fig. 5.

Fig. 11 shows in schematic form a further variant of the device for generating second harmonic radiation in fig. 6.

Fig. 12 shows in schematic form a further variant of the device for generating second harmonic radiation in fig. 8 a.

Fig. 13a,13b, 13c show a further embodiment according to the invention produced by a combination of the previously indicated embodiments.

Detailed Description

Description of one or more preferred embodiments according to the invention with reference to the above-mentioned figures, the reference numeral 1 denotes in its entirety an apparatus for generating second harmonic radiation from fundamental frequency radiation according to the invention.

The device comprises one or more nonlinear crystals C which fulfill the condition of second harmonic generation SHG by non-critical phase matching, wherein the electromagnetic fields of fundamental frequency radiation and second harmonic radiation pass more than once together through one or more nonlinear optical crystals.

In particular, if a single nonlinear crystal is provided, the fundamental radiation is passed through said nonlinear crystal C a plurality of times. Or if several nonlinear crystals are provided, passing the fundamental radiation through said nonlinear crystals at least once. In the latter case, the nonlinear crystals are arranged in series with each other with respect to the propagation direction of the fundamental radiation.

It should be noted that the fundamental radiation passes through one or more nonlinear crystals C (in this case they are arranged in series) to produce second harmonic radiation having a frequency twice the frequency of the fundamental radiation.

Thus, the second harmonic radiation is generated as a result of the fundamental radiation passing through one or more nonlinear crystals C.

The device further comprises an optical phase actuator a located upstream or downstream of the nonlinear crystal C with respect to the optical axis of the nonlinear crystal (in any case along the propagation direction of the fundamental radiation) and configured to control the relative phase between a fundamental electromagnetic field E _ω present at an angular frequency ω of the fundamental radiation and a second harmonic electromagnetic field E _2ω of an angular frequency 2ω derived as a result of the latter passing through the nonlinear crystal(s) CAnd the field also passes through the optical phase actuator a.

In other words, the phase actuator a is configured to act on a phase mismatch between the fundamental frequency radiation and the second harmonic radiation.

It should be noted that both fundamental radiation and second harmonic radiation pass through the same actuator a.

In other words, the arrangement enables the relative phase between fundamental radiation and second harmonic to be controlled as they travel along the same optical path.

In particular, the subject of the present invention relates to a method for generating second harmonic radiation from fundamental frequency radiation, said method being characterized in that it comprises a step of controlling parameters of said optical actuator a.

This control is achieved by managing the temperature of the optical actuator a itself, or by applying an electric or magnetic field to said optical actuator a. The parameters of the optical actuator a that are changed include their effective geometrical extent and/or refractive index with respect to angular frequencies ω and 2ω, and/or the relative phaseThe actuator may be produced by, for example, a birefringent crystal, also made of the same material and cut with the same orientation as the nonlinear crystal used for frequency doubling.

The further method comprises the step of varying one or more of said parameters of said optical actuator a over time by controlling the temperature of the optical actuator a itself, or by applying an electric or magnetic field to said optical actuator a.

Furthermore, the method comprises performing a plurality of measurements of power associated with second harmonic radiation, varying one or more of said parameters of said optical actuator a over time, after nonlinear power conversion of said fundamental electromagnetic field E _ω from angular frequency ω to angular frequency 2ω and after passage of said second harmonic electromagnetic field E _2ω through said nonlinear optical crystal C and said optical actuator a. Values in the parameters of the optical actuator a are then determined for which the measured power is maximum relative to the power measured during the multiple performed measurements.

Preferably, the step of varying one or more of said parameters of said optical actuator a over time is performed by controlling the temperature of the optical actuator a itself. The temperature is adjusted to introduce a change in refractive index according to the relationship Δn=n_ω (T) -n_2ω (T) in order to compensate for the relative phaseAnd thus optimize the second harmonic generation process in crystals used for this purpose, where Δn represents the difference in refractive index, n_ω (T) represents the refractive index associated with the fundamental frequency at temperature T, and n_2ω (T) represents the refractive index associated with the second harmonic at temperature T.

There is a direct relationship between the difference in refractive index or equivalent optical path and the relative phase shift. Thus, controlling the parameters of the actuator means controlling the relative phaseFor example, the objective is to optimize the nonlinear conversion of power from angular frequency ω to angular frequency 2ω in a configuration where the fundamental radiation and the second harmonic field together pass through the nonlinear optical crystal multiple times. This allows maximizing the optical power available during the second harmonic generation without using resonant optical elements.

Preferably, the method comprises providing a concave mirror S downstream of the optical actuator a and the nonlinear optical crystal C, according to the main propagation direction of said radiation, such that said output radiation is reflected back by the concave mirror S and passes through said optical actuator a and said nonlinear optical crystal C again.

Note that in this specification, the propagation direction may also coincide with the main optical axis O.

Fig. 3a (first variant of the first alternative embodiment) shows a schematic diagram of a device in which a nonlinear crystal C is present, suitable for generating second harmonic electromagnetic radiation (SHG) from an initial incident field E ((0)) _, ω. At the output end of the crystal C, there are fields E++1 ((1)) -2ω with an angular frequency 2ω in addition to those with an angular frequency ω ((1)) - ω. The temperature t_c of the crystal is controlled so as to operate under temperature phase matching (non-critical phase matching) conditions such that n_ω (t_c) =n_2ω (t_c).

Fig. 3a shows a first embodiment in which the mirror has its own optical axis aligned with respect to the main optical axis O of the nonlinear optical crystal C, such that the output radiation is reflected back by the concave mirror S according to a direction aligned with respect to the main optical axis O. The curvature and distance of the mirror are selected in such a way that a focusing condition is obtained that maximizes the SHG conversion efficiency in order to maximize the power associated with the final SHG field E++2.

To compensate for the phase shift that may accumulate between E ((1)). Omega. And E ((1)). Omega. 2. Omega. Due to various factors including air propagation, specular reflection, thermal effects in crystals, etcAn actuator A is introduced which can be controlled by acting on external parametersThe actuator may for example consist of a birefringent crystal such as LBO (lithium triborate). The temperature t_a of the actuator a does not have to satisfy the phase matching condition of a. It must be able to introduce a variation in refractive index Δn=n_ω (T) -n_2ω (T) to compensateThereby optimizing the SHG process in the crystal used for this purpose. To avoid accumulating the relative phase on both wavefronts (i.e. the dependence of the relative phase with respect to the wave vector in the lateral direction), Δn < <1 is suggested. Therefore, it is preferable that the actuator is made of the same material as the nonlinear crystal satisfying the non-critical phase matching condition and has the same cut.

Fig. 3b shows a second variant of fig. 3a, in which the light reflected back by the mirror is slightly misaligned. The principle of operation is not modified.

In this variant embodiment, the concave mirror S has its own optical axis inclined at a predetermined angle with respect to the main optical axis O, so that said output radiation is reflected back by the concave mirror according to a direction of misalignment of the main optical axis O of the nonlinear optical crystal, so as to pass through a portion of said nonlinear optical crystal C which is different from the portion of said fundamental radiation that passes through the same nonlinear optical crystal for the first time.

According to a further embodiment, the method comprises providing a plurality of nonlinear crystals C _i and C _i+1, each aligned according to their main optical axis O, and inserting at least one optical actuator between two of them. The relative phase between the fundamental electromagnetic field and the second harmonic field at the entrance of each nonlinear crystal is controlled by the optical actuator a. According to one possible embodiment of the invention, one optical actuator a is inserted between each pair of nonlinear crystals C _i and C _i+1 for each ith crystal.

Fig. 5 (first variant of the second alternative embodiment) shows an actuator a consisting of a temperature-controlled birefringent medium (t_a) capable of compensating any phase shift between the fields E ≡c ((1)) _ -2 ω before entering the next crystal, for example due to an anti-reflective coating.

According to a second variant of the second embodiment in fig. 5, the method comprises inserting a focusing element F between said nonlinear crystals C _i and C _i+1 for focusing the radiation according to the main optical axis O in the nonlinear crystal located behind said focusing element.

In particular, the focusing element (F) is produced by a lens made of birefringent material such that the refractive indices of the electromagnetic fields E _ω and E _2ω are the same, n _ω＝n_2ω, the method comprising adjusting the temperature T _lens of the lens so as to be able to focus not only the radiation in the SHG crystal, but also to control the phase shiftTo perform the function of the phase actuator a.

Specifically, in fig. 6, one or both of the input and output surfaces of actuator a are optically configured such that the field is focused like a lens. The temperature of the lens T_lens of the device is controlled in order to simultaneously control the phase shiftAnd a focal point allowing the laser beam to refocus in each subsequent crystal. To limit chromatic aberration, such a device is used to control relative phaseAnd at the same time the means for focusing the fields are preferably produced from a material for which the refractive indices of the fundamental frequency field and the SHG field are identical, except for the phase delay required for fine tuning control of the phase shift. If the optical axis is cut in the proper direction orientation, a material producing a nonlinear crystal can meet this requirement.

According to a third embodiment of the invention shown in fig. 8a and 8b, it is shown how at least one of said nonlinear crystals C _i and C _i+1 has at least one optical aperture cut with a radius of curvature in order to focus the optical field. Preferably, both optical apertures of at least one of the nonlinear crystals C _i and C _i+1 are cut with a radius of curvature in order to focus the optical field. Advantageously, there is no dispersion problem due to the phase matching properties of the crystalline material.

This further embodiment is shown generally in fig. 7, wherein, in order to maximize the frequency doubling efficiency in each crystal, one or both faces of the nonlinear crystal are cut with a radius of curvature in order to obtain the function of the lens in fig. 6, thereby limiting the divergence of the light beam and thus facilitating focusing of the light on the same crystal (e.g. c_1) or on successive nonlinear crystals c_2, c_3..c_n.

In particular, in fig. 8a an actuator a is added, consisting of a temperature-tuned birefringent dispersive medium, in order to control the phase shift input to the next crystalIn fig. 8b, the actuator also has an optical aperture cut with a radius of curvature to focus the light inside it.

Fig. 9-13 show further variants produced by the combination of the previous solutions, extending to multiple crystals.

In particular, fig. 13a, 13b, 13c show the embodiment represented in fig. 10, in which the length of the device has been reduced due to the insertion of a concave mirror between the nonlinear crystal and the subsequent actuator (or vice versa).

In general, it should be noted that the nonlinear crystals for Second Harmonic Generation (SHG) shown in fig. 5-10 are all intended for use under temperature-tuned, non-critical phase-matching conditions, and that for this purpose there is an independent temperature control t_c for each crystal.

The attached figures also comprise fig. 1, which shows a basic solution according to the prior art, in which the electromagnetic field propagates twice in the nonlinear crystal by back reflection on a concave mirror.

Fig. 2 shows the use of Periodically Poled Crystals (PPCs) under quasi-phase matching conditions in a configuration as shown in fig. 1, according to the prior art. In this configuration, the exit face of the nonlinear crystal is not parallel to the entrance face. The length of the optical path can be varied by translating the crystal in a direction perpendicular to the optical axis. This enables correction of any phase shift between the electromagnetic fields e_ω and e_2ω on the second pass of the crystal.

Fig. 4 shows a schematic diagram of an apparatus in which a plurality of nonlinear crystals (C1, C2) are arranged in order to obtain higher SHG conversion efficiency. This configuration makes it possible to circumvent the technical limitations typical in the production of large-size crystals. The optical aperture of each crystal may be provided with an anti-reflection coating.

The temperature of each crystal is independently controlled, and the temperature t_ (Ci) (in this case, i=1, 2) of each crystal is varied to optimize phase matching.

The incident electromagnetic field is focused in the central part of the device, with a rayleigh range z_r, e.g. satisfying the conversion optimization relationship z_r≡l/3, where L is the total length of the crystal series.

The subject of the invention is also a device 1 implementing the above-described process, which is therefore also fully cited herein for the device 1.

Claims (13)

1. A method for generating second harmonic radiation from a fundamental frequency radiation having its own predetermined frequency, comprising the following steps: providing one or more nonlinear crystals (C) arranged in series along the propagation direction of the fundamental frequency radiation, the one or more nonlinear crystals (C) satisfying the conditions for second harmonic generation (SHG) by non-critical phase matching, Passing the same fundamental frequency radiation through the one or more nonlinear crystals (C) so as to generate second harmonic radiation having a frequency twice the predetermined frequency of the fundamental frequency radiation after the fundamental frequency radiation passes through the one or more nonlinear crystals (C), wherein the electromagnetic fields (E) of the fundamental frequency and the second harmonic of the radiation also pass through the one or more nonlinear optical crystals together; if a single nonlinear crystal is provided, passing the fundamental frequency radiation through the nonlinear crystal (C) multiple times so that the nonlinear crystal (C) is passed multiple times by the optical path of the fundamental frequency radiation and the second harmonic radiation, or if a plurality of nonlinear crystals are provided, passing the fundamental frequency radiation through the nonlinear crystal (C) at least once so that the optical path of the fundamental frequency radiation and the second harmonic radiation extends to the inside of each nonlinear crystal (C); An optical phase actuator (A) is provided, which is positioned along the propagation direction of the fundamental radiation and through which both the fundamental radiation and the second harmonic radiation pass; the optical phase actuator (A) is configured to control the relative phase between the fundamental electromagnetic field (E _ω ) and the second harmonic electromagnetic field (E _2ω ) wherein the fundamental electromagnetic field (E _ω ) has an angular frequency (ω) of the fundamental radiation, the second harmonic electromagnetic field (E _2ω ) has an angular frequency (2ω) derived from the fundamental radiation as a result of the fundamental radiation passing through the one or more nonlinear crystals (C) and also passing through the optical phase actuator (A), Characterized in that the method comprises the step of controlling the parameters of the optical actuator (A) by controlling the temperature of the optical actuator (A) itself, or by applying an electric field or a magnetic field to the optical actuator (A), wherein the parameters of the optical actuator (A) include its effective geometric range and/or refractive index relative to the angular frequency (ω) and (2ω), and/or the parameters affecting the relative phase ( ) parameters; the method also includes: a step of varying one or more of said parameters of said optical actuator (A) over time by controlling the temperature of said optical actuator (A) itself, or by applying an electric field or a magnetic field to said optical actuator (A), When the fundamental frequency electromagnetic field (E _ω ) and the second harmonic electromagnetic field (E _2ω ) pass together through the nonlinear optical crystal (C) and the optical actuator (A), after nonlinear power conversion from the angular frequency (ω) to the angular frequency (2ω), performing multiple measurements of the power associated with the second harmonic radiation, varying one or more of the parameters of the optical actuator (A) over time; The parameter of the optical actuator (A) is determined for which the measured power is a maximum relative to powers measured during performance of the plurality of measurements. 2. A method according to claim 1, characterized in that said step of varying one or more of said parameters of said optical actuator (A) over time is performed by controlling the temperature of said optical actuator (A) itself; said temperature being adjusted to introduce a variation of the refractive index according to the relationship Δn=n_ω(T)-n_2ω(T) in order to compensate said relative phase ( ), and thereby optimize the second harmonic generation process in a crystal for this purpose, where Δn represents the difference in refractive index, n_ω(T) represents the refractive index associated with the fundamental frequency at the temperature (T) of the crystal, and n_2ω(T) represents the refractive index associated with the second harmonic at the temperature (T) of the crystal. 3. The method according to claim 1 is characterized in that, if a single nonlinear crystal (C) is provided, a concave mirror (S) is provided, and the concave mirror (S) is located downstream of the optical actuator (A) and the nonlinear optical crystal (C) according to the propagation direction of the fundamental frequency radiation, so that the output radiation is reflected back by the concave mirror (S) and passes through the optical actuator (A) and the nonlinear optical crystal (C) again. 4. A method according to claim 3, wherein the mirror has its own optical axis, which is aligned relative to the main optical axis (O) of the nonlinear optical crystal (C), so that the output radiation is reflected back by the concave mirror (S) according to the direction aligned relative to the main optical axis (O). 5. The method according to claim 3, wherein the concave mirror (S) has its own optical axis, which is inclined at a predetermined angle relative to the main optical axis (O) of the nonlinear optical crystal (C), so that the output radiation is reflected back by the concave mirror according to a direction that is not aligned with the main optical axis (O) of the nonlinear optical crystal, and passes through a part of the nonlinear optical crystal (C), which is different from the part of the fundamental frequency radiation that passes through the same nonlinear optical crystal (C) for the first time. 6. Method according to claim 1, characterized in that a plurality of nonlinear crystals ( _Ci ) and (Ci ₊₁ ) are provided, the plurality of nonlinear crystals ( _Ci ) and (Ci ₊₁ ) being aligned according to the main propagation direction of the radiation and at least one optical actuator (A) being inserted between at least two of them; the method envisages that the relative phase between the fundamental frequency electromagnetic field and the second harmonic field at the entrance of each nonlinear crystal (C) is controlled by means of the optical actuator (A). 7. The method according to claim 6, characterized in that it comprises the step of inserting a focusing element (F) between the nonlinear crystals (C _i ) and (C _i+1 ), the focusing element (F) being used to focus the radiation in the nonlinear crystal (C) located after the focusing element according to the main propagation direction of the radiation. 8. The method according to claim 7, wherein the focusing element (F) is produced by a lens made of birefringent material so that the refractive index of the electromagnetic fields (E _ω ) and (E _2ω ) is the same: n _ω =n _2ω ; the method comprises adjusting the temperature of the lens (T _lens ) in order not only to focus the radiation in the SHG crystal but also to control the phase shift To realize the function of the phase actuator (A). 9. The method according to any of the preceding claims, wherein at least one of the nonlinear crystals ( _Ci ) and (Ci ₊₁ ) has at least one optical aperture cut with a radius of curvature in order to focus an optical field entering the crystal or to collimate an optical field leaving the crystal. 10. The method according to claim 9, wherein at least one of the nonlinear crystals ( _Ci ) and (Ci ₊₁ ) has two optical apertures cut with a radius of curvature in order to focus and/or collimate the optical field. 11. The method according to claim 1, characterized in that the method is implemented without using a resonant cavity or an optical resonator, and without using a resonant optical cavity. 12. A method according to any preceding claim, characterised in that the actuator (A) is arranged to control the relative phase between the fundamental radiation and the second harmonic when they travel along the same optical path. 13. An apparatus for generating second harmonic radiation from fundamental frequency radiation, comprising: one or more nonlinear crystals (C) arranged in series along the propagation direction of the fundamental frequency radiation, the one or more nonlinear crystals (C) satisfying the conditions for second harmonic generation (SHG) by noncritical phase matching, wherein if a single nonlinear crystal is provided, the electromagnetic fields of the radiated fundamental frequency and second harmonic are passed through the nonlinear crystal (C) multiple times, or if a plurality of nonlinear crystals are provided, the fundamental frequency radiation is passed through the nonlinear crystal (C) at least once; an optical phase actuator (A) positioned along the propagation direction of the fundamental radiation and through which both the fundamental radiation and the second harmonic radiation pass; the optical phase actuator (A) being configured to control the relative phase between the fundamental electromagnetic field (E _ω ) and the second harmonic electromagnetic field (E _2ω ) wherein the fundamental electromagnetic field (E _ω ) has an angular frequency (ω) of the fundamental radiation, the second harmonic electromagnetic field (E _2ω ) has an angular frequency (2ω) derived from the fundamental radiation as a result of the fundamental radiation passing through the one or more nonlinear crystals (C) and also passing through the optical phase actuator (A), Characterized in that the optical phase actuator (A) is configured to change its parameters according to what is defined in one or more of the preceding claims.